{"paper":{"title":"Scalable Gaussian Process Computations Using Hierarchical Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.OC"],"primary_cat":"stat.CO","authors_text":"Christopher J. Geoga, Michael L. Stein, Mihai Anitescu","submitted_at":"2018-08-09T16:04:25Z","abstract_excerpt":"We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its gradient and Hessian, as well as the expected Fisher information matrix, that are computable in quasilinear $O(n \\log^2 n)$ complexity for a large range of models. To accomplish this, we (i) choose a specific hierarchical approximation for covariance matrices that enables the computation of their exact derivatives and (ii) use a stabilized form of the Hutchinson st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03215","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}